Quantum control based on solid-state nuclear magnetic resonance and its applications

ZHAO Liqiang; LI Yuchen; YIN Haochuan; ZHANG Shengyu; WU Ze; PENG Xinhua

doi:10.7498/aps.74.20241709

Abstract

Solid-state nuclear magnetic resonance (NMR) has emerged as an important technique for material characterization, finding extensive applications across a diverse range of disciplines including physics, materials science, chemistry, and biology. Its utility stems from the ability to probe the local atomic environments and molecular dynamics within solid materials, which provides information on the composition of the material. In recent years, the scope of solid-state NMR has expanded into the realm of quantum information science and technology, where its abundant many-body interactions pulse control methodologies make it have significant research value and application potential. This paper offers a comprehensive overview of the research objects and theoretical underpinnings of solid-state NMR, delving into the critical nuclear spin interaction mechanisms and their corresponding Hamiltonian forms. These interactions, which include dipolar coupling, chemical shift anisotropy, and quadrupolar interactions, are fundamental to the interpretation of NMR spectra and the understanding of material properties at the atomic level. Moreover, the paper introduces typical dynamical control methods employed in the manipulation of solid-state nuclear spins. Techniques such as dynamical decoupling, which mitigates the effects of spin-spin interactions to extend coherence times, and magic-angle spinning, which averages out anisotropic interactions to yield high-resolution spectra. These methods are essential for enhancing the sensitivity and resolution of NMR experiments, enabling the extraction of detailed structural and dynamic information from complex materials. Then we introduce some recent advancements in quantum control based on solid-state NMR, such as nuclear spin polarization enhancement techniques, which include dynamic nuclear polarization (DNP) and cross polarization (CP), significantly boost the sensitivity of NMR measurements. Additionally, the control techniques of Floquet average Hamiltonians are mentioned, showcasing their role in the precise manipulation of quantum states and the realization of quantum dynamics. Finally, the paper presents a series of seminal research works that illustrate the application of solid-state NMR quantum control technologies in the field of quantum simulation. These studies demonstrate how solid-state NMR can be leveraged to simulate and investigate quantum many-body systems, providing valuable insights into quantum phase transitions, entanglement dynamics, and other phenomena relevant to quantum information science. By bridging the gap between fundamental research and practical applications, solid-state NMR continues to play a crucial role in advancing our understanding of quantum materials and technologies.

Keywords:

solid-state nuclear magnetic resonance /
quantum control /
nuclear spin interactions /
quantum simulation

Authors and contacts

1.
CAS Key Laboratory of Microscale Magnetic Resonance and Department of Modern Physics, University of Science and Technology of China, Hefei 230026, China
2.
CAS Center for Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei 230026, China
3.
Hefei National Laboratory, Hefei 230088, China
4.
Department of Physics, The Chinese University of Hong Kong, Hong Kong 999077, China

Corresponding author: WU Ze, wuze@ustc.edu.cn ; PENG Xinhua, xhpeng@ustc.edu.cn

Funds: Project supported by the Innovation Program for Quantum Science and Technology (Grant No. 2021ZD0303205), the National Natural Science Foundation of China (Grant No. 12261160569), the National Natural Science Foundation of China/Hong Kong RGC Collaborative Research Scheme (Grant No. CUHK401/22), the New Cornerstone Science Foundation, the China Postdoctoral Science Foundation (Grant No. 2023M733416), and the Fundamental Research Funds for the Central Universities (Grant No. WK2030000084).

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References

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Cited By

图 1 (a) 金刚烷样品分子示意图; (b) 氟磷灰石样品原子排布示意图

Figure 1. (a) Schematic diagram of adamantane molecule; (b) schematic diagram of the atomic configuration of a fluoroapatite sample.

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图 2 交叉极化的脉冲序列图^[38]　(a) HHCP; (b) DOCP; (c) ADCP; (d) AD/DO-CP

Figure 2. Pulse sequences of cross polarization^[38]: (a) HHCP; (b) DOCP; (c) ADCP; (d) AD/DO-CP.

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图 3 16脉冲序列

Figure 3. 16-pulse sequence

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图 4 Magic echo序列^[111]

Figure 4. Magic echo sequence^[111]

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图 5 WAHUHA序列^[112]

Figure 5. WAHUHA sequence^[112]

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图 6 魔角旋转示意图

Figure 6. Schematic diagram of magic angle spinning

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图 7 魔角旋转条件下的偶极恢复脉冲序列^[44]

Figure 7. Pulse sequence of dipolar recovery at the magic angle^[44].

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图 8 测量多量子相干的脉冲序列

Figure 8. Pulse sequence for measurement of multiple quantum coherences

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表 1 利用8脉冲序列实现不同目标哈密顿量所对应的脉冲欧拉角设置

Table 1. Setup of the Euler angles of 8-pulse sequences for realizing different target Hamiltonians

$ \hat{H}_{\rm tar} $	C	单位(π), $ n=1, 2, 3, 4 $
$ \displaystyle\sum_{i<j}J_{ij}[2\hat{I}^i_z\hat{I}^j_z-\hat{I}^i_x\hat{I}^j_x-\hat{I}^i_y\hat{I}^j_y] $	1	$ \beta_{n}=1, \gamma_n= {(n-1)}/{2} $
	–0.5	$ \beta_{n} = {1}/{2}, \gamma_n = {(n-1)}/{2} $
$ \displaystyle\sum_{i<j}J_{ij}[\hat{I}^i_x\hat{I}^j_x-\hat{I}^i_y\hat{I}^j_y] $	1	$ \beta_{n}=0.304, \gamma_n= [{1+4(-1)^n}]/{4} $
	–1	$ \beta_{n}=0.304, \gamma_n= [{3+4(-1)^n}]/{4} $
$ \displaystyle\sum_{i<j}J_{ij}[\hat{I}^i_z\hat{I}^j_x+\hat{I}^i_x\hat{I}^j_z] $	1/3	$ \beta_{n}=0.304, \gamma_n= [{3(-1)^n}]/{4} $
	–1/3	$ \beta_{n}=0.304, \gamma_n= {(-1)^n}/{4} $
$ \displaystyle\sum_{i<j}J_{ij}[\hat{I}^i_z\hat{I}^j_y+\hat{I}^i_y\hat{I}^j_z] $	1/3	$ \beta_{n}=0.304, \gamma_n = [{2+(-1)^n}]/{4} $
	–1/3	$ \beta_{n}=0.304, \gamma_n= [{2+(-1)^n}]/({-4}) $
$ \displaystyle\sum_{i<j}J_{ij}[\hat{I}^i_y\hat{I}^j_x+\hat{I}^i_x\hat{I}^j_y] $	1	$ \beta_{n}=0.304, \gamma_n= [{1+(-1)^n}]/{2} $
	–1	$ \beta_{n}=0.304, \gamma_n = [{2+(-1)^n}]/{2} $

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[2]	DiVincenzo D P 1995 Phys. Rev. A 51 1015 Google Scholar
[3]	Cory D G, Fahmy A F, Havel T F 1997 P. Natl. A. Sci. 94 1634 Google Scholar
[4]	Gershenfeld N A, Chuang I L 1997 Science 275 350 Google Scholar
[5]	Jones J A 2011 Progress Nucl. Mag. Res. Sp. 59 91 Google Scholar
[6]	Vandersypen L M, Chuang I L 2004 Rev. Mod. Phys. 76 1037 Google Scholar
[7]	Khaneja N, Reiss T, Kehlet C, Schulte-Herbrüggen T, Glaser S J 2005 J. Magn. Reson. 172 296 Google Scholar
[8]	Haeberlen U 2012 High Resolution NMR in Solids Selective Averaging: Supplement 1 Advances in Magnetic Resonance (Vol. 1) (Elsevier) pp1–186
[9]	Kane B E 1998 Nature 393 133 Google Scholar
[10]	Pham L M, DeVience S J, Casola F, Lovchinsky I, Sushkov A O, Bersin E, Lee J, Urbach E, Cappellaro P, Park H, et al. 2016 Phys. Rev. B 93 045425 Google Scholar
[11]	Gärttner M, Bohnet J G, Safavi-Naini A, Wall M L, Bollinger J J, Rey A M 2017 Nat. Phys. 13 781 Google Scholar
[12]	Geier S, Thaicharoen N, Hainaut C, Franz T, Salzinger A, Tebben A, Grimshandl D, Zürn G, Weidemüller M 2021 Science 374 1149 Google Scholar
[13]	Miller C, Carroll A N, Lin J, Hirzler H, Gao H, Zhou H, Lukin M D, Ye J 2024 Nature 633 332 Google Scholar
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[18]	Cappellaro P, Emerson J, Boulant N, Ramanathan C, Lloyd S, Cory D G 2005 Phys. Rev. Lett. 94 020502 Google Scholar
[19]	Álvarez G A, Suter D, Kaiser R 2015 Science 349 846 Google Scholar
[20]	Wei K X, Ramanathan C, Cappellaro P 2018 Phys. Rev. Lett. 120 070501 Google Scholar
[21]	Rovny J, Blum R L, Barrett S E 2018 Physical review letters 120 180603 Google Scholar
[22]	Wei K X, Peng P, Shtanko O, Marvian I, Lloyd S, Ramanathan C, Cappellaro P 2019 Phys. Rev. Lett. 123 090605 Google Scholar
[23]	Sánchez C M, Chattah A K, Wei K X, Buljubasich L, Cappellaro P, Pastawski H M 2020 Phys. Rev. Lett. 124 030601 Google Scholar
[24]	Peng P, Yin C, Huang X, Ramanathan C, Cappellaro P 2021 Nat. Phys. 17 444 Google Scholar
[25]	Peng P, Ye B, Yao N Y, Cappellaro P 2023 Nat. Phys. 19 1027 Google Scholar
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[31]	Kaur G, Cappellaro P 2012 New J. Phys. 14 083005 Google Scholar
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